Trick question since the whole theory is that no object with mass can travel at the speed. (Photons qualify as something else) Although...If you're using the Flash comic book as your resource. When you hit the speed of light like the Flash did in a certain issue, you'd become an energy source, just like him, and therefore would no longer have headlights. Simplified, but there you have it.
What height should you aim your driving lights at? Seriously..I need to know if I have them aimed too high.
Michael